Find the time constant for the given circuit.

When the key $K$ is pressed at time $t = 0$, which of the following statements about the current $I$ in the resistor $AB$ of the given circuit is true?

$A$ capacitor of capacitance $C$ is connected in series with a resistance $R$ and a $DC$ source of $emf$ $E$ through a key. The capacitor starts charging when the key is closed. By the time the capacitor has been fully charged, what amount of energy is dissipated in the resistance $R$?

Three identical capacitors are given a charge $Q$ each and they are then allowed to discharge through resistances $R_1, R_2,$ and $R_3$. Their charges,as a function of time,are shown in the graph below. The smallest of the three resistances is

$A$ capacitor of capacity $0.1 \mu F$ connected in series to a resistor of $10 M \Omega$ is charged to a certain potential and then made to discharge through the resistor. The time in which the potential will take to fall to half its original value is (Given, $\log _{10} 2=0.3010$ ) (in $\,s$)

The plates of a capacitor are charged to a potential difference of $V \, \text{volts}$ and then connected across a resistor. The potential difference across the capacitor decreases exponentially with respect to time. After one second, the potential difference between the plates is $V/3$; then after two seconds from the start, the potential difference between the plates is